Why does my mesh flatten on the X-axis in the game engine?
Select your object and press CtrlA -> Apply Scale. This will set scale of both objects to 1.0, 1.0, 1.0.

Before you applied the scale, you must have scaled the objects along the X-Axis at one point. This will change the dimensions of the object, but the scale will be something like: 5.0, 1.0, 1.0. This won't change much in the 3D view, but BGE will reset all scales to 1.0 which (as you noticed) causes issues.